
Chapter 2
Review of Literature
Kalman Filter has been an area of research for several decades and various papers have
been published on it. While working on this project we referred to - Constrained Nonlinear State
Estimation Using Ensemble Kalman Filters [2] and Constrained nonlinear state estimation based
on the UKF approach [3] .
The key takeaways from the first paper [2] were :
● Proposed a constrained recursive formulation of the ensemble Kalman filter (EnKF) that
retains the advantages of unconstrained EnKF while systematically dealing with bounds
on the estimated state variables.
● The performance of the proposed constrained EnKF is compared with the performances
obtained using the recursive constrained formulations available in the literature using two
benchmark examples from the literature (a gas-phase reactor and an isothermal batch
reactor), which involve constraints on the estimated state variables.
● When compared, the performance of the proposed C-EnKF formulation was found to be
significantly better than those obtained using RNDDR and C-UKF formulations.
Furthermore, the performance of the proposed C-EnKF scheme was found to be
satisfactory when employed for state estimation in a system having constraints on process
noise.
The key takeaways from the second paper [3] were :
● Overview of several UKF based nonlinear estimation algorithms as an alternative to the
EKF
● Suggested a reformulation of the correction step which can be applied to all of the
presented UKF algorithms, presented a QP formulation of the NLP UKF (which also can
be applied to all of the presented UKF algorithms)
● Proposed alternatives to realize constraints within the UKF approach